Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

Exploring the Application Effect of Flipped Classroom Combined with Problem-Based Learning Teaching Method in Clinical Skills Teaching of Standardized Training for Resident Doctors of Traditional Chinese Medicine

Objective: To explore the application effect of flipped classroom combined with problem-based learning teaching method in clinical skills teaching of standardized training for resident doctors of traditional Chinese Medicine. Methods: The study used the experimental control method. The study lasted from September to November 2022. The subjects of this study were 49 students of standardized training for resident doctors of traditional Chinese Medicine from grades 2020, 2021 and 2022 of Dazhou integrated TCM & Western Medicine Hospital. They were randomly divided into experiment group (25) and control group (24). The experiment group adopted flipped classroom combined with problem-based learning teaching method, and the control group adopted traditional teaching method. The teaching content was 4 basic clinical skill projects, including four diagnoses of traditional Chinese Medicine, cardiopulmonary resuscitation, dressing change procedure, acupuncture and massage. The evaluation method was carried out by comparing the students’ performance and a self-designed questionnaire was used to investigate the students’ evaluation of the teaching method. Results: The test scores of total scores in the experimental group (90.12 ± 5.89) were all higher than those in the control group (81.47 ± 7.96) (t = 4.53, P P Conclusions: The teaching process of the flipped classroom combined with problem-based learning teaching method is conducive to improving the efficiency of classroom teaching, cultivating students’ self-learning ability, and enhancing students’ willingness to learn.

Study of Axisymmetric Infinite Guide Lined with Locally Reacting Material without Flow Using DtN Operators

The present work proposed a new method for the modeling by the finite element method of the acoustic propagation problems in infinite axisymmetric cylindrical guides lined with locally reacting absorbent materials without flow. The method deals with the development of an efficient transparent boundary condition based on DtN operators. The method developed in this study is successfully applied to a straight axisymmetric lined guide by imposing a mode on one of the artificial boundaries of the truncated guide. The results are in good agreement with analytical solutions. Applying the method for a non-uniform axisymmetric lined guide which is a complex case, proved its effectiveness and the results compared to those of PML layers are in very good agreement.

Research and Practice of the Blended Teaching Model of BOPPPS Teaching Method Under the Background of Digital Education: Taking Operations Research Course as an Example

The rapid development of digital education provides new opportunities and challenges for teaching model innovation.This study aims to explore the application of the BOPPPS(Bridge-in,Objective,Pre-assessment,Participatory learning,Post-assessment,Summary)teaching method in the development of a blended teaching model for the Operations Research course under the background of digital education.In response to the characteristics of the course and the needs of the student group,the teaching design is reconstructed with a student-centered approach,increasing practical teaching links,improving the assessment and evaluation system,and effectively implementing it in conjunction with digital educational technology.This teaching model has shown significant effectiveness in the context of digital education,providing valuable experience and insights for the innovation of the Operations Research course.

Aggregation operators and CRITIC-VIKOR method for confidence complex q-rung orthopair normal fuzzy information and their applications

Supply chain management is an essential part of an organisation's sustainable programme.Understanding the concentration of natural environment,public,and economic influence and feasibility of your suppliers and purchasers is becoming progressively familiar as all industries are moving towards a massive sustainable potential.To handle such sort of developments in supply chain management the involvement of fuzzy settings and their generalisations is playing an important role.Keeping in mind this role,the aim of this study is to analyse the role and involvement of complex q-rung orthopair normal fuzzy(CQRONF)information in supply chain management.The major impact of this theory is to analyse the notion of confidence CQRONF weighted averaging,confidence CQRONF ordered weighted averaging,confidence CQRONF hybrid averaging,confidence CQRONF weighted geometric,confidence CQRONF ordered weighted geometric,confidence CQRONF hybrid geometric operators and try to diagnose various properties and results.Furthermore,with the help of the CRITIC and VIKOR models,we diagnosed the novel theory of the CQRONF-CRITIC-VIKOR model to check the sensitivity analysis of the initiated method.Moreover,in the availability of diagnosed operators,we constructed a multi-attribute decision-making tool for finding a beneficial sustainable supplier to handle complex dilemmas.Finally,the initiated operator's efficiency is proved by comparative analysis.

Effectiveness of Participatory Teaching Methods in the Standardized Training of Respiratory Medicine Residents

Objective:To explore and analyze the application effect of participatory teaching method in the standardized training of respiratory medicine residents.Methods:The study period was from May 2022 to May 2023.20 doctors in the standardized training of respiratory medicine residency in our hospital were taken as research subjects and grouped into the participatory group(n=10)and the routine group(n=10)by using the random number lottery method.The participatory group practised participatory teaching methods,and the routine group practised routine teaching methods.The results of discharge assessment,teaching evaluation,and mini-Clinical Evaluation Exercise(mini-CEX)assessment were compared between the groups.Results:The theoretical assessment,operational assessment,and total scores of the participatory group were significantly higher than those of the routine group,and the difference was statistically significant(P<0.05).The teaching evaluation of independent learning,theoretical mastery,teamwork,clinical thinking,communication,and learning interest of the participatory group was significantly higher than that of the routine group,and the difference was statistically significant(P<0.05).The mini-CEX assessments of history inquiry,organizational effectiveness,professionalism,physical examination,clinical diagnosis,communication skills,and overall clinical competence of the participatory group were significantly better than those of the routine group,and the difference was statistically significant(P<0.05).The teaching satisfaction of the participatory group was significantly higher than that of the routine group,the difference was statistically significant(P<0.05).Conclusion:Participatory teaching methods can improve the overall level of doctors in the respiratory medicine residency standardized training,and the teaching satisfaction is improved.

Symplectic partitioned Runge-Kutta method based onthe eighth-order nearly analytic discrete operator and its wavefield simulations

We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.

A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem

A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the context of nonlocal operators.The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity,which is necessary for the eigenvalue analysis such as the waveguide problem.The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields.The governing equations are converted into nonlocal integral form.An hourglass energy functional is introduced for the elimination of zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems.

Using Different Standardized Methods for Species Identification:A Case Study Using Beaks from Three Ommastrephid Species

The cephalopod beak is a vital hard structure with a stable configuration and has been widely used for the identification of cephalopod species. This study was conducted to determine the best standardization method for identifying different species by measuring 12 morphological variables of the beaks of Illex argentinus, Ommastrephes bartramii, and Dosidicus gigas that were collected by Chinese jigging vessels. To remove the effects of size, these morphometric variables were standardized using three methods. The average ratios of the upper beak morphological variables and upper crest length of O. bartramii and D. gigas were found to be greater than those of I. argentinus. However, for lower beaks, only the average of LRL(lower rostrum length)/LCL(lower crest length), LRW(lower rostrum width)/LCL, and LLWL(lower lateral wall length)/LCL of O. bartramii and D. gigas were greater than those of I. argentinus. The ratios of beak morphological variables and crest length were found to be all significantly different among the three species(P < 0.001). Among the three standardization methods, the correct classification rate of stepwise discriminant analysis(SDA) was the highest using the ratios of beak morphological variables and crest length. Compared with hood length, the correct classification rate was slightly higher when using beak variables standardized by crest length using an allometric model. The correct classification rate of the lower beak was also found to be greater than that of the upper beak. This study indicates that the ratios of beak morphological variables to crest length could be used for interspecies and intraspecies identification. Meanwhile, the lower beak variables were found to be more effective than upper beak variables in classifying beaks found in the stomachs of predators.

ITERATIVE REGULARIZATION METHODS FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS WITH M-ACCRETIVE MAPPINGS IN BANACH SPACES

In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.

GALERKIN-PETROV METHODS OF TOEPLITZ OPERATORS ON DIRICHLET SPACE

The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that such methods converge if the basis and test function own certain circular symmetry.

Multilevel Iteration Methods for Solving Linear Operator Equations of the First Kind

In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework.

Calculating the Number of Pregnant Women Receiving Standardized Services for PMTCT of HIV in Liangshan Prefecture,Based on the Equivalent Method

Objective To calculate the number of pregnant women who receive standardized prevention of mother-to-child transmission(PMTCT)services for HIV annually.Methods HIV-positive pregnant women in six counties of Liangshan Prefecture in 2017 were selected as study subjects.The entire process,from when the subjects first received the PMTCT of HIV services to the end,was divided into four stages,which were further divided into 25 phases.The equivalent coefficient was used to indicate the weight of workload in each phase.Seven experts were invited to score the equivalent coefficient;the number of pregnant women who received standardized services to prevent the transmission of HIV was calculated.Results A total of 663 HIV-positive pregnant women were registered in six Liangshan Prefecture counties in 2017.This figure was converted into 7,780 person-months devoted to HIV-positive pregnant women,with 260 person-months(3.34%)spent on the first antenatal care,1,510 person-months(19.41%)during pregnancy,378 person-months(4.86%)on delivery,and 5,632 person-months(72.39%)on post-partum period.The equivalent coefficient calculation showed that 314 HIV-positive pregnant women received standardized PMTCT services.Conclusion The number of pregnant women receiving standardized services for the PMTCT of HIV can be calculated accurately using the equivalent method to identify the gap between the level of PMTCT of HIV intervention services needed and the actual workload.

On the Stable Method Computing Values of Unbounded Operators

Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.

Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method

In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.

Inspiration of Foreign Innovative Drug Pricing Methods and Medical Insurance Payment Standards to China

Objective To study the innovative drug pricing methods and medical insurance payment standards in foreign countries and to provide reference for China’s government.Methods The official websites were searched for information and related literature,and literature review was used.Results and Conclusion In foreign countries,the clinical value of innovative drugs and their impact on medical insurance funds were comprehensively evaluated based on factors such as quality-adjusted life years,clinical benefit,and improvement of clinical benefit.Then,the evaluation results were taken as an important basis for whether innovative drugs were admitted to the medical insurance catalog and establishing medical insurance payment standards.By using international experience for reference,innovative drug pricing methods and medical insurance payment standards for China’s national conditions can be improved by establishing a basic database of clinical value and drug economic evaluation of innovative drugs,as well as innovative drug payment models based on decision thresholds.

The Efficacy and Safety of Dinoprostone Vaginal Insert for Labor Induction Following Optimization of Standard Operating Procedure: A Retrospective Study in China

Background:The study aimed to assess the efficacy and safety of dinoprostone vaginal insert in labor induction following optimization of standard operating procedure(SOP)and to discover independent predictors of vaginal delivery.Methods:This study comprised 551 pregnant women who required cervical ripening with dinoprostone before induction of labor.Using univariate and multivariate analyses,independent predictors of vaginal delivery were identified.Results:443 of the 551 women(80.4%)gave birth vaginally.Vaginal delivery was predicted by maternal age(24-30 vs.<24,P<0.001;30-35 vs.<24,P=0.03),gestational age(P=0.005),birth weight(P<0.001),parity(P=0.001),pre-pregnancy BMI(P<0.001),premature rupture of membranes(P=0.001),meconium-stained amniotic fluid(P<0.001),fundal height(P<0.001)and the Bishop score(P<0.001).None of the women exhibited severe postpartum hemorrhage.Conclusions:The maternal age,gestational age,birth weight,parity,body mass index,premature membrane rupture,amniotic fluid contamination,fundal height,and the Bishop score were independent predictors of vaginal delivery.These may guide the clinical use of dinoprostone for induction of labor.

INCOMPLETE SEMI-ITERATIVE METHODS FOR SOLVING SINGULAR LINEAR OPERATOR EQUATIONS IN BANACH SPACE WITH APPLICATIONS IN MARKOV CHAIN MODELING

We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent has a pole of order k at the point 1. Sufficient conditions for the convergence of ISIM to a solution of x=Tx+c, where c belongs to the range space of R(I-T) k, are established. We show that the ISIM has an attractive feature that it is usually convergent even when the spectral radius of the operator T is greater than 1 and Ind 1T≥1. Applications in finite Markov chain is considered and illustrative examples are reported, showing the convergence rate of the ISIM is very high.

Solving Energy Levels for SSH Hamiltonian Describing Peierls Phase Transition by Virtue of Invariant Eigen-operator Method

<Abstract>We show that the recently proposed invariant eigen-operator (lEO) method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition.The electronic energy band of compound lattice is also studied by IEO method.

ELEMENT FUNCTIONS OF DISCRETE OPERATOR DIFFERENCE METHOD

The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.